The constitutive relation of cushion material is often simplified to be ideal cubic nonlinear and hyperbolic nonlinear in solving packaging dynamics. Due to the finiteness of cushion material is neglected, the exact response is difficult to obtain. The stress of cushion material can reach infinity when the cushion material being compressed to be extreme position, so it avoid the infiniteness of cushion material by using tangent function to express the special mechanical phenomenon. The numerical examples show the response of packaging system can exceed the extreme position even the thickness of the material if not considering the constrained conditions, and the optimized packaging structure can not be available; the error results are disappeared when tangent function is involved to modify the constitutive relationships.